Chemically-strengthened glass articles, also known as ion-strengthened glass articles, are used in a variety of applications. For example, chemically-strengthened glasses are widely used as touch screens for hand-held consumer electronics such as smart phones and tablets.
In broad overview, chemically-strengthened glass articles are made by forming a glass having a composition suitable for chemical strengthening into a desired configuration, e.g., into a glass sheet in the case of faceplates, and then subjecting the formed glass to chemical strengthening through an ion-exchange (IOX) process, e.g., a treatment in which the formed glass is submersed in a salt bath at an elevated temperature for a predetermined period of time.
The IOX process causes ions from the salt bath, e.g., potassium ions, to diffuse into the glass while ions from the glass, e.g., sodium ions, diffuse out of the glass. Because of their different ionic radii, this exchange of ions between the glass and the salt bath results in the formation of a compressive layer at the surface of the glass which enhances the glass's mechanical properties, e.g., its surface hardness. The effects of the ion exchange process are typically characterized in terms of two parameters: (1) the depth of layer (DOL) produced by the process and (2) the final maximum surface compressive stress (CS). Values for these parameters are most conveniently determined using optical measurements, and commercial equipment is available for this purpose.
For most applications of chemically-strengthened glass articles and, in particular, for consumer applications, articles with a high fracture strength, a high resistance to contact damage, and a high surface flaw tolerance are desired. A high fracture strength means that the article can withstand substantial levels of mechanical impact without fracturing. A high resistance to contact damage and a high surface flaw tolerance mean that the article can withstand substantial levels of surface damage without a catastrophic failure.
These latter surface properties are particularly desirable because, in practice, the presence of surface defects, such as flaws and cracks, has been found to be one of the major causes for glass failure. Consequently, the robustness of a chemically-strengthened glass article in the hands of a consumer turns out to be dependent on the handling and processing conditions the article experienced during manufacture. To reduce the costs associated with “gentle” manufacturing, glass articles that are resistant to surface damage and are tolerant of surface flaws are thus desired since such resistance and tolerance reduces the effects of surface conditions on the ultimate strength of the article.
Developing chemical strengthening protocols that achieve a high fracture strength, a high resistance to contact damage, and a high tolerance to surface flaws has proved challenging. Indeed, conventional one-step ion-exchange (IOX) processes do not always improve glass strength reliability. Instead, as reported by K. Matsuno, K. Shukuri, T. Nakazumi, K. Matsumoto, and K. Sono, paper 25-G-87F presented at the Glass Division of the American Ceramic Society, Fall Meeting, Bedford Springs, Pa., 30 Sep. to 2 Oct. 1987, strength variation can increase after ion exchange in silicate glass. Some studies have appeared in the literature regarding the use of double ion exchange (DIOX) processes to improve glass properties. See D. J. Green, R. Tandon, and V. M. Sglavo, Crack arrest and multiple cracking in glass through the use of designed residual stress profiles, Science, 283, 1295 (1999); and V. M. Sglavo, A. Prezzi, and D. J. Green, In situ observation of crack propagation in ESP (engineered stress profile) glass, Eng. Frac. Mech., 74, 1383 (2007). However, these studies have had a limited scope and have not provided generally-applicable methods for obtaining quantitative information for the complex ion diffusion kinetics that result when multiple ion-diffusion treatments are applied to a glass article in order to improve its ultimate properties.
Analytic solutions to the diffusion equations are available for only a limited set of geometries and limited sets of boundary and initial conditions. See, for example, Crank, J. The Mathematics of Diffusion (2nd ed.), Oxford: Oxford University Press, 1975. Ion-diffusion treatments which may be desirable for chemically-strengthening glass articles generally have complex boundary and initial conditions and are not mathematically solvable in closed form. Also, the programming effort needed to handle the wide range of boundary and initial conditions that can be envisioned is daunting. Indeed, the complexity, cost, and time commitments associated with such an effort can rival those associated with the historical brute-force approach of performing multiple ion-diffusion treatments and then measuring the resulting concentration profiles.
The art has thus been faced with a lack of a practical methodology for dealing with the complex compositional profiles and ion kinetics that result from ion-diffusion treatments. Without quantitative information regarding the ion diffusion kinetics associated with chemical-strengthening, glass engineers have been working under a significant handicap when designing chemical-strengthening protocols.
The present disclosure addresses this existing problem in the art and provides computer-implemented techniques for calculating concentration profiles and diffusion kinetics of ions in glass articles during ion-diffusion treatments and, in particular, during multiple, sequential, ion-diffusion treatments. As shown by the examples set forth below, the techniques require only limited user input, employ efficient numerical calculations, and can handle the wide variety of ion-diffusion conditions that glass engineers may envision for improving the properties of chemically-strengthened glass articles.